cocoPit {coconots}

Probability Integral Transform Based Model Assessment Procedure

Description

Computes the probability integral transform (PIT) and provides the non-randomized PIT histogram for assessing absolute performance of a fitted model as proposed by Czado et al. (2009).

Usage

cocoPit(coco, J = 10, conf.alpha = 0.05, julia = FALSE)

Arguments

coco

An object of class coco

J

Number of bins for the histogram (default: 10)

conf.alpha

Confidence level for the confidence bands.

julia

if TRUE, the PIT is computed with Julia.

Details

The adequacy of a distributional assumption for a model is checked by checking the cumulative non-randomized PIT distribution for uniformity. A useful graphical device is the PIT histogram, which displays this distribution to J equally spaced bins. We supplement the graph by incorporating approximately 100(1 - \alpha)\% confidence intervals obtained from a standard chi-square goodness-of-fit test of the null hypothesis that the J bins of the histogram are drawn from a uniform distribution. For details, see Jung, McCabe and Tremayne (2016).

Value

an object of class cocoPit. It contains the The probability integral transform values, its p-values and information on the model specifications.

Author(s)

Manuel Huth

References

Czado, C., Gneiting, T. and Held, L. (2009) Predictive model assessment for count data. Biometrics 65, 1254–61.

Jung, Robert C., Brendan P. M. McCabe, and Andrew R. Tremayne. (2016). Model validation and diagnostics. In Handbook of Discrete Valued Time Series. Edited by Richard A. Davis, Scott H. Holan, Robert Lund and Nalini Ravishanker. Boca Raton: Chapman and Hall, pp. 189–218.

Jung, R. C. and Tremayne, A. R. (2011) Convolution-closed models for count time series with applications. Journal of Time Series Analysis, 32, 3, 268–280.

Examples

lambda <- 1
alpha <- 0.4
set.seed(12345)
data <- cocoSim(order = 1, type = "Poisson", par = c(lambda, alpha), length = 100)
#julia_installed = TRUE ensures that the fit object
#is compatible with the julia cocoPit implementation 
fit <- cocoReg(order = 1, type = "Poisson", data = data)

#PIT R implementation
pit_r <- cocoPit(fit)